Abstract: We prove some category theoretic results for -sets much in the spirit of Vaught and Burgess. Since the proofs entail many results on -sets and the -operator, we have studied them in some detail and have formulated many results appropriate for our purpose in, perhaps, a more unified manner than is available in the literature. Our main theorem is the following: Any -set in the product of two Polish spaces can be approximated, in category, uniformly over all sections, by sets generated by rectangles with one side an -set and the other a Borel set. In fact, we prove a levelwise version of this result. For -sets, this has been proved by V. V. Srivatsa.